Get lattice points' positions at specific frame when animated by another object (through hook modifiers)
Depending on how many hooks there are a (probably too tedious solution) would be to create a vertex group containing only that vertex for each hook. Then you can get those from script.
Selecting the vertices for a hook modifier has always been an enigma to me, which I don't like. 

If any of the hook modifiers has a strength &lt; 1, the method of using it's hook object's location will fail.

A fairly brute force solution can be found here: How do I get the deformed coordinate of a vertex with Python?
remember the vertices of a lattice are called points.

A Similarly brute force solution would be to copy your lattice, apply the modifiers, read the applied vert info and then delete the object again.

All those solutions are fairly ugly, but it's all I can come up with atm.

For meshes, bmesh offers a solution of copying the modifier's info to a temp mesh: https://blenderartists.org/t/get-vertices-coordinate-after-deformation/617992
Don't know if you can transfer that to a lattice.

Also: you don't have to multiply .matrix_world with anything. It gives you the absolute position (and loc/rot), no matter what parenting/constraints are influencing it.